MSCE Additional Mathematics study plan

Expand and simplify algebraic expressions involving surds, indices, and partial fractions, completing at least 20 graded examples.

Solve quadratic equations and inequalities by factorising, completing the square, and using the discriminant to classify roots.

Apply the factor and remainder theorems to find unknown coefficients in polynomials and fully factorise cubics.

Solve simultaneous equations, including one linear and one non-linear, and interpret the number of solutions graphically.

Differentiate polynomials, products, quotients, and composite functions using chain, product, and quotient rules.

Solve problems on gradients, tangents, normals, and stationary points with second-derivative classification.

Integrate powers of x, including negative and fractional indices, and evaluate definite integrals.

Connect the chain rule to rates of change and small increments, applying them to applied problems.

Integrate using substitution and recognise when a logarithmic or trigonometric standard form applies.

Find areas under curves and between curves, and volumes of revolution about the x-axis.

Apply integration to kinematics, converting between displacement, velocity, and acceleration by differentiating and integrating.

Solve differential equations of the form dy/dx = f(x)g(y) by separating variables with initial conditions.

Sketch graphs of quadratic, cubic, exponential, logarithmic, and trigonometric functions, marking intercepts, asymptotes, and turning points.

Determine domain and range, and identify whether a function is one-to-one, even, odd, or periodic.

Find and evaluate composite and inverse functions algebraically and verify them graphically.

Apply coordinate geometry to find equations of lines, perpendicular bisectors, circles, and intersection points.

Use arithmetic and geometric progressions to find nth terms and sums, including sums to infinity where convergent.

Apply the binomial theorem to expand expressions with positive integer and rational powers, finding specific terms.

Solve trigonometric equations in given intervals using identities and the CAST/quadrant method.

Prove and apply identities including Pythagorean, double-angle, and compound-angle forms.

Solve triangles using the sine and cosine rules and calculate areas, including the ambiguous case.

Work with radian measure, arc length, sector area, and small-angle approximations.

Perform vector addition, subtraction, and scalar multiplication in two and three dimensions, and calculate magnitude and unit vectors.

Use the scalar product to find angles between vectors and solve perpendicularity and line-intersection problems.

Carry out matrix addition, multiplication, and inversion, and solve 2x2 and 3x3 linear systems using matrices.

Apply transformation matrices to describe rotations, reflections, enlargements, and stretches, and combine transformations.

Compute probabilities using tree diagrams, Venn diagrams, and conditional probability rules.

Calculate and interpret mean, median, mode, variance, and standard deviation for grouped and ungrouped data.

Consolidate the highest-weight algebra and calculus topics through full past-paper-style questions under timed conditions.

Diagnose recurring error patterns from weeks 1-7 and rework every flagged question to full marks.

Practise exam technique: reading command words, allocating time per mark, and showing method marks.

Build a final revision sheet of the 20 formulas and results most often forgotten.